Let a be an irrational number. Is (1)/(a) rational or irrational? Choose 1 answer: (A) Rational (B) Irrational (c) It can be either rational or irrational

Evaluate Reciprocal of Irrational Number: Evaluate the nature of the reciprocal of an irrational number. If a is an irrational number, then by definition, it cannot be expressed as a ratio of two integers. The reciprocal of a number is 1 divided by that number. So, the reciprocal of a is 1/a.Determine Rationality of 1/a: Determine if 1/a is rational or irrational. If a is irrational, then 1/a is also not expressible as a ratio of two integers, because there is no integer that can be multiplied by a to yield the integer 1 (since a is not an integer). Therefore, 1/a is also irrational.Consider Exceptions or Special Cases: Consider any exceptions or special cases. There are no exceptions in this case; the reciprocal of an irrational number does not become rational simply by taking its reciprocal.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Let
a be an irrational number. Is
(1)/(a) rational or irrational?
Choose 1 answer:
(A) Rational
(B) Irrational
(c) It can be either rational or irrational

Let $a$ be an irrational number. Is $\frac{1}{a}$ rational or irrational? $\newline$ Choose $1$ answer: $\newline$ (A) Rational $\newline$ (B) Irrational $\newline$ (C) It can be either rational or irrational

View step-by-step help

Home

Math Problems

Algebra 2

Classify rational and irrational numbers

Full solution

Q. Let

a

be an irrational number. Is

\frac{1}{a}

rational or irrational?

\newline

Choose

1

answer:

\newline

(A) Rational

\newline

(B) Irrational

\newline

Evaluate Reciprocal of Irrational Number: Evaluate the nature of the reciprocal of an irrational number. $\newline$ If $a$ is an irrational number, then by definition, it cannot be expressed as a ratio of two integers. The reciprocal of a number is $1$ divided by that number. So, the reciprocal of $a$ is $\frac{1}{a}$ .
Determine Rationality of $\frac{1}{a}$ : Determine if $\frac{1}{a}$ is rational or irrational. $\newline$ If $a$ is irrational, then $\frac{1}{a}$ is also not expressible as a ratio of two integers, because there is no integer that can be multiplied by $a$ to yield the integer $1$ (since $a$ is not an integer). Therefore, $\frac{1}{a}$ is also irrational.
Consider Exceptions or Special Cases: Consider any exceptions or special cases. $\newline$ There are no exceptions in this case; the reciprocal of an irrational number does not become rational simply by taking its reciprocal.